Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly-interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an
inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant $d$. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta $pm (pi/2) (hbar / d)$ in the momentum distribution function.
One of the pivotal questions in the physics of high-temperature superconductors is whether the low-energy dynamics of the charge carriers is mediated by bosons with a characteristic timescale. This issue has remained elusive since electronic correlat
ions are expected to dramatically speed up the electron-boson scattering processes, confining them to the very femtosecond timescale that is hard to access even with state-of-the-art ultrafast techniques. Here we simultaneously push the time resolution and the frequency range of transient reflectivity measurements up to an unprecedented level that enables us to directly observe the 16 fs build-up of the effective electron-boson interaction in hole-doped copper oxides. This extremely fast timescale is in agreement with numerical calculations based on the t-J model and the repulsive Hubbard model, in which the relaxation of the photo-excited charges is achieved via inelastic scattering with short-range antiferromagnetic excitations.
We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the non-equilibrium dynamics in an interacting many-body system where exces
s energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the non-equilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines so-called optimal phonon modes. We discuss their structure in non-equilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.
Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site an
d is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.
Determination of the parameter regime in which two holes in the t-J model form a bound state represents a long standing open problem in the field of strongly correlated systems. By applying and systematically improving the exact diagonalization metho
d defined over a limited functional space (EDLFS), we show that the average distance between two holes scales as $langle d rangle sim 2 (J/t)^{-1/4}$ for J/t < 0.15, therefore providing strong evidence that two holes in the t-J model form the bound state for any nonzero J/t. However, the symmetry of such bound pair in the ground state is p-wave. This state is consistent with phase separation at finite hole filling, as observed in a recent study [Maska et al, Phys. Rev. B 85, 245113 (2012)].
We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators e
xpand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion: The asymptotic density dynamics is identical to that of initially localized, non-interacting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this non-equilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model: While being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the non-interacting limit. These results are compared to the set-up of a recent experiment [PRL 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways: While the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.
